Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2
We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the def...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Pleiades Publishing
2011
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| Online Access: | http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf |
| _version_ | 1825644211796443136 |
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| author | Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author_facet | Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor |
| author_sort | Accardi, Luigi |
| collection | IIUM |
| description | We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as
the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree.
For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain i.e., we show that the state is independent of the boundary conditions. |
| first_indexed | 2024-03-05T22:29:39Z |
| format | Article |
| id | oai:generic.eprints.org:1614 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T22:29:39Z |
| publishDate | 2011 |
| publisher | Pleiades Publishing |
| record_format | dspace |
| spelling | oai:generic.eprints.org:16142013-06-28T01:24:14Z http://irep.iium.edu.my/1614/ Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor QA Mathematics We propose the construction of a quantum Markov chain that corresponds to a “forward” quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY -model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain i.e., we show that the state is independent of the boundary conditions. Pleiades Publishing 2011-02-17 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf Accardi, Luigi and Mukhamedov, Farrukh and Saburov, Mansoor (2011) Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2. Mathematical Notes, 90 (2). pp. 8-20. ISSN 0001-4346 http://www.springerlink.com/content/0001-4346 10.1134/S0001434611070029 |
| spellingShingle | QA Mathematics Accardi, Luigi Mukhamedov, Farrukh Saburov, Mansoor Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title | Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title_full | Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title_fullStr | Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title_full_unstemmed | Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title_short | Uniqueness of quantum Markov chains associated with an XY -model on a Cayley tree of order 2 |
| title_sort | uniqueness of quantum markov chains associated with an xy model on a cayley tree of order 2 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1614/1/acmfsm-MatNotes%282011%29.pdf |
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